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        <h1>Discriminant Ranges for Number Fields</h1>


<p>The database consists of fields from two sources:
<ul>
<li>The PARI database from the Bordeaux PARI group
<li>Additional totally real fields of degrees from 6 to 10 computed by
  John Voight.
</ul>
</p>

<p>
<ul>
<li>PARI database discriminant ranges.  It is possible that the
  discriminant range depends further on the signature, but this is not
  shown here.
<p>
<table border=1 cellpadding=5 class='right_align_table'>
<tr>
<th>degree</th>
<th>minimum discriminant</th>
<th>maximum discriminant</th>
</tr>
<tr><td>1<td>\(1\)<td>\(1\)</tr>
<tr><td>2<td>\(-10^6\)<td>\(10^6\)</tr>
<tr><td>3<td>\(-10^6\)<td>\(2\cdot10^6\)</tr>
<tr><td>4<td>\(-10^6\)<td>\(10^6\)</tr>
<tr><td>5<td>\(-10^6\)<td>\(2\cdot10^7\)</tr>
<tr><td>6<td>\(-10^6\)<td>\(10^7\)</tr>
<tr><td>7<td>\(-11841551\)<td>\(149324209\)</tr>
</table>
</p>
<li>Voight database additional discriminant ranges.  For degrees up to
  9, the database contains all totally real fields with discriminant
  in the given range.
<p>
<table border=1 cellpadding=5 class='right_align_table'>
<tr>
<th>degree</th>
<th>minimum discriminant</th>
<th>maximum discriminant</th>
</tr>
<tr><td>6<td>\(1\)<td>\(16771805\)</tr>
<tr><td>7<td>\(1\)<td>\(213873729\)</tr>
<tr><td>8<td>\(1\)<td>\(2556640000\)</tr>
<tr><td>9<td>\(1\)<td>\(25405254289\)</tr>
<tr><td>10<td>\(1\)<td>\(7623696325213\)</tr>
</table>
</p>
</ul>
</p>

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